In order to maximise the modularity \(m\) , Newman [1]} proposed to define \(y_{i}=1\) , in case \((z_{1})_{i}>0\) , otherwise \(y_{i} = -1\) . In a next iteration, the same procedure of spectral division into two partitions is repeated on both sub-graphs. However, using only the block sub-matrix of \(M\) , corresponding to cluster \(g\)  in next iteration would not take into account inter-community links. Instead, for the estimated cluster \(g\) , the modularity matrix \(M_{g}\)  is updated as
\(M_{g} = m_{ij} - \left(\sum _{k\in g}m_{ik}\right)\cdot \delta _{ij},\) 
